WASHINGTON — Senate Democrats have one particular judge’s name in mind as they await the identity of President Trump’s Supreme Court nominee: Merrick B. Garland.

Democrats and their allies remain furious that Senate Republicans refused to even consider Judge Garland, President Barack Obama’s nominee to the high court, with 10 months remaining in Mr. Obama’s second term. That deep resentment is certain to color their handling of Mr. Trump’s choice just as it has contributed to their resistance to moving quickly on Mr. Trump’s cabinet selections.

All indications are that they see the forthcoming nomination as a chance to take a strong stand against the new president, since they still have the power to filibuster a Supreme Court choice — at least for now.

“I haven’t seen the names,” said Senator Patrick J. Leahy, Democrat of Vermont and a veteran of multiple Supreme Court fights. “But when they had a consensus person with Merrick Garland, every single Republican who raised their hand and solemnly swore before God to uphold the Constitution refused to follow the Constitution and even have a hearing.”

Top Democrats say they don’t intend to play “tit for tat” with the nomination. But they say they will insist on what they consider to be a mainstream candidate capable of securing at least the 60 votes needed to thwart any filibuster. Otherwise, they promise to do whatever they can to block the nominee.

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Merrick B. Garland was former President Barack Obama’s nominee to fill Antonin Scalia’s seat on the Supreme Court.CreditZach Gibson/The New York Times

“We are not going to do what the Republicans did,” said Senator Chuck Schumer of New York, the Democratic leader, “but if the candidate’s out of the mainstream, I can tell you I will fight and my caucus will fight tooth and nail against them.”

The chief reason that Democrats will not do what the Republicans did is that they can’t — Republicans remain in the Senate majority, which last year enabled them to refuse to even schedule a hearing and now gives them control over the confirmation process. But unlike with cabinet nominees, Democrats could still employ a filibuster against a Supreme Court pick, because the high court was excluded from a 2013 change engineered by Democrats to thwart filibusters against lower-court nominees.

If Democrats hold out, Senator Mitch McConnell of Kentucky, the majority leader, will no doubt come under pressure to wipe out the possibility of filibuster against Supreme Court nominees. Given the steps Republicans were willing to take to hold open the vacancy created by the death of Antonin Scalia, Democrats believe Senate Republicans might choose to eliminate that filibuster power, too.

“All the signals are there is no limit to what they are capable of doing to give the big special interests behind them control of the court,” said Senator Sheldon Whitehouse of Rhode Island, a Democratic member of the Judiciary Committee.

But Republicans are already differentiating their handling of Mr. Garland’s nomination from whatever is to come with the announcement by Mr. Trump. They argue that the situations are not comparable, given the timing of the presidential election.

“There’s a big difference between not approving a Supreme Court nominee in the middle of a highly contested presidential election, and the beginning of a four-year term,” Mr. McConnell said on Tuesday, noting that Republicans did not filibuster Supreme Court nominees in the first term of either President Bill Clinton or Mr. Obama. Mr. McConnell took pains on Tuesday to note that both Republicans and Democrats were invited to the White House to discuss the coming nomination with Mr. Trump as part of the requirement for seeking the Senate’s advice and consent.

Many Republicans and their conservative allies would prefer not to abolish the filibuster on Supreme Court nominees, knowing that it could come back to haunt them by allowing a future Democratic majority a free hand — essentially the same reason Democrats left high court nominees out of the 2013 change. It is also unclear whether Republicans would even have the votes to do so through a simple majority vote on an arcane procedural maneuver. But the question will hang over the entire confirmation fight and could force a showdown.

If the Democrats filibuster, “ then I guess we’ll see what steps need to be taken at the time,” said Senator John Thune of South Dakota, a member of the Republican leadership. “But I think the one thing that we’re committed to is getting a Supreme Court justice confirmed.”

Democrats say that one result of the stalemate over Judge Garland is that it has shown that the Supreme Court can function, though imperfectly, without a full complement of nine members, relieving the party of some guilt for keeping the court short-handed if it comes to that over a Trump nominee.

Senator Richard Blumenthal, a Connecticut Democrat who sits on the Judiciary Committee, said Democrats were also galvanized by the turnout at last weekend’s protests. He said it would serve as a unifying force for Senate Democrats.

“That swell of people and strength and spirit at the marches we had Saturday showed us we have the American populace on our side,” Mr. Blumenthal said. “They understand the importance of the Supreme Court to those issues that brought them to the streets, principally women.”

Mr. Blumenthal said the selection of a nominee by President Trump would “put a face and a voice” on the Supreme Court battle. But for now, the face and voice most Democrats are putting on the coming clash are those belonging to Judge Garland.